Theory of linear and integer programming
Theory of linear and integer programming
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IEEE Transactions on Computers
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IEEE Transactions on Computers
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Journal of the ACM (JACM)
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ISCA '84 Proceedings of the 11th annual international symposium on Computer architecture
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ACM Transactions on Design Automation of Electronic Systems (TODAES)
Scheduling and partitioning for multiple loop nests
Proceedings of the 14th international symposium on Systems synthesis
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CASES '01 Proceedings of the 2001 international conference on Compilers, architecture, and synthesis for embedded systems
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Highly parallel computaions
Partitioning Loops with Variable Dependence Distances
ICPP '00 Proceedings of the Proceedings of the 2000 International Conference on Parallel Processing
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ACM Transactions on Design Automation of Electronic Systems (TODAES)
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ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
Guidance of Loop Ordering for Reduced Memory Usage in Signal Processing Applications
Journal of Signal Processing Systems
Embedded Systems Design
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This paper deals with the problem of transforming irregular data dependence structures of algorithms with nested loops into more regular ones. Algorithms under consideration are n-dimensional algorithms (algorithms with n nested loops) with affine dependences where dependences are affine functions of index variables of the loop. Methods are proposed to uniformize affine dependence algorithms, i.e., to transform affine dependence algorithms into uniform dependence algorithms where dependences are independent of the index variables (constant). Objectives are considered to guide the selection of feasible uniformizations. The first one is to reduce the number of dependences after uniformization. The second one is to maximize parallelism preserved by the uniformization. Some parallelism might be lost due to the uniformization. The parallelism preserved by the uniformization is measured by 1) the total execution time by the optimal linear schedule which assigns each computation in the algorithm an execution time according to a linear function of the index of the computation, and 2) the size of the cone spanned by the dependence vectors after uniformization.